This paper addresses high-resolution ultrasonic image reconstruction from Full Matrix Capture (FMC) data in the context of nondestructive testing (NDT). In order to reduce the numerical complexity, the time-domain data and ultrasonic model are projected into the image domain through a linear beamforming procedure. The resulting model is interpreted as a shift-variant convolution process, affected by non-stationary and colored noise. An interpolation procedure is built in order to account for the spatial variations of the resulting point spread function. Under the same methodological framework, an approximate whitening filter is proposed and incorporated in the forward model. Both constructions then allow fast computations and limited memory storage. Deconvolution is performed by minimizing the least-squares data misfit error, with a penalization term favoring sparsity and spatial continuity of the output images. Results with synthetic data show that the proposed approach gives performances close to the inversion of raw FMC data, while being computationally much more efficient. The method is finally applied to laboratory data for the inspection of a stainless steel block containing closely spaced and small sidedrilled holes calibrated flaws. Successful detection and separation is achieved for flaws with diameters six times smaller than the wavelength, and distant from each other by four times less than the resolution limit given by the Rayleigh criterion.